nLab machine learning




Machine learning is a branch of computer science which devises algorithms to learn from data so as to perform tasks without being explicitly programmed to do so. Notable approaches include neural networks, support vector machines and Bayesian networks.


Classical machine learning

For a treatment in terms of category theory see

See also:

With regards to kernel methods:

Quantum machine learning

In view of quantum computation (ie. quantum machine learning):

  • Diego Ristè, Marcus P. da Silva, Colm A. Ryan, Andrew W. Cross, Antonio D. Córcoles, John A. Smolin, Jay M. Gambetta, Jerry M. Chow & Blake R. Johnson,

    Demonstration of quantum advantage in machine learning, npj Quantum Information volume 3, Article number: 16 (2017) (doi:10.1038/s41534-017-0017-3)

  • Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd, Quantum Machine Learning, Nature 549 (2017) 195–202 (doi:10.1038/nature23474)

    EurekaAlert, Quantum Machine Learning 14-Sep-2017

  • Iris Cong, Soonwon Choi, Mikhail D. Lukin, Quantum convolutional neural networks, Nature Physics volume 15, pages 1273–1278 (2019) (doi:10.1038/s41567-019-0648-8)

    (on quantum neural networks)

  • Yunchao Liu, Srinivasan Arunachalam, Kristan Temme, A rigorous and robust quantum speed-up in supervised machine learning (arXiv:2010.02174)

  • Melanie Swan, Renato P dos Santos, Frank Witte, Between Science and Economics, Volume 2: Quantum Computing Physics, Blockchains, and Deep Learning Smart Networks, World Scientific 2020 (doi:10.1142/q0243)

  • Stefano Mangini, Francesco Tacchino, Dario Gerace, Daniele Bajoni, Chiara Macchiavello, Quantum computing models for artificial neural networks, EPL (Europhysics Letters) 134(1), 10002 (2021) (arXiv:2102.03879)

and with emphasis on classically controlled NISQ-computes:


There are or will be innumerable applications. Here are some:

To mathematical structures in algebraic geometry, representation theory, number theory and combinatorics:

reviewed in:

To the conformal bootstrap:


Last revised on February 6, 2023 at 10:31:56. See the history of this page for a list of all contributions to it.